This reasoning works for a fully between group design. If this interval includes 0, then the interaction is not significantly different from zero. Finally, find the range in which 95% of the MIC found are located. Repeat this a very large number of times (say 5,000). Thus, to do a boostrap estimate, sub-samples in the groups with replacement, and compute MIC. Defining the first increment as $d_1$ and the second as $d_2$, the means are thus As of treatment, the same occur (treatment measures are a few point above control measures). If such is the case, mean in $b$ is a few points above mean in $a$, and mean in $c$ is also the same amount of points above the mean in $d$. If MIC is zero, it means that there is a main effect of questions (there is an increase-or decrease- from Q1 to Q2), a main effect of conditions (there is an increase -or decrease- from control to treatment) and no interaction. It quantifies the amount of non-additivity in the dataset. The mean interaction contrast (MIC) is given by The conditions $a$ and $b$ are the question factor for the treatment and $c$ and $d$ are the question factor for the control condition. Let define the four conditions as a, b, c and d. In a 2 x 2 design, it is fairly easy to run a bootstrap test of the interaction. Therefore, I am looking for nonparametric equivalents to ANOVA for these two designs. However, the problem is that my data deviate strikingly from normality (in fact, so do the residuals). Normally, I would conduct repeated measures ANOVAs for these experiments. I am interested in the potential interactions between the two factors (question and treatment). That is, it is a repeated measures 2x2 design participants are asked four questions that encode the two manipulations in a factorial form: Q1Treatment1, Q1Treatment2, Q2Treatment1, and Q2Treatment2. The second experiment is identical, except for that the design becomes completely within-subjects. That is, participants are asked two questions in the experiment (Q1 and Q2), while a factor varies systematically between the two groups (Treatment1 and Treatment2). The first experiment is a mixed 2x2 design, with one between-subject factor (treatment) and one within-subject factor (question). The dependent variable is a rating provided by the participant, that is, an integer number from 0 to 100. I have run two psychological experiments.
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